Quantum Gravity and Relativistic Astrophysics

这项研究涉及两类问题，涉及不同的方法，但统一于广义相对论的共同根源，即爱因斯坦的引力理论。其中一组问题集中在广义相对论的天体物理学方面，特别是黑洞和引力波，其中很大一部分是由确定黑洞相互作用产生的引力波信号的问题引起的。该方法将涉及数值和符号计算，但不会直接涉及在超级计算机上求解全套爱因斯坦方程。相反，将使用解析和近似方法来寻找和理解引力波输出。另一组问题旨在理解爱因斯坦理论的正则量子化。黑洞再次成为人们关注的中心，现在处于亚微观尺度。半经典地说，它们是通过霍金辐射蒸发的。为了超越半经典描述，微超空间量子化将被应用于一些球对称模型。从正则数据重建特权时空坐标有望在概念和技术层面上简化量子理论。对这些模型的研究应该澄清这样的问题，比如量子理论中的视界奇点和曲率奇点会发生什么。

The research described spans two classes of problems which involve different methods, but which are unified by the common roots in general relativity, Einstein's theory of gravitation. One set of problems is centered on astrophysical facets of general relativity, especially black holes and gravitational waves, and much of it is motivated by the problem of determining the gravitational wave signal produced by black hole interactions. The approach will involve numerical and symbolic computation, but will not directly involve solving the full set of Einstein equations on supercomputers. Rather, analytic and approximation methods will be used to find and understand gravitational wave outputs. Another set of problems aims at understanding the canonical quantization of Einstein's theory. Black holes are again at the center of attention, now at the submicroscopic scale. Semiclassically, they evaporate by Hawking radiation. To go beyond the semiclassical description, midisuperspace quantization will be applied to a number of spherically symmetric models. It is expected that the reconstruction of privileged spacetime coordinates from the canonical data will simplify the quantum theory both at the conceptual and technical levels. A study of these models should clarify such questions as what happens to the horizon and curvature singularities in quantum theory.